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Vibrational frequency scaling factors


Calculated vibrational frequencies ("theory" in table) are calculated at B3LYP/cc-pVQZ
Scale factor How many Source
Molecules Vibrations
0.969 ± 0.021 115 344 cccbdb
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Formula Name Mode Symmetry Frequency Count
Theory Experiment ratio molecules vibrations
H2 Hydrogen diatomic 1 Σg 4416 4161 0.942 1 1
LiH Lithium Hydride 1 Σ 1407 1360 0.966 2 2
Li2 Lithium diatomic 1 Σg 346 346 1.002 3 3
NaH sodium hydride 1 Σ 1158 1133 0.979 4 4
Na2 Sodium diatomic 1 Σg 162 158 0.971 5 5
BeH beryllium monohydride 1 Σ 2066 1987 0.962 6 6
MgH magnesium monohydride 1 Σ 1457 1432 0.983 7 7
BH Boron monohydride 1 Σ 2350 2269 0.966 8 8
AlH aluminum monohydride 1 Σ 1645 1625 0.988 9 9
CH Methylidyne 1 Σ 3048     10 10
C2 Carbon diatomic 1 Σg 1875 1827 0.975 11 11
SiH Silylidyne 1 Σ 2022 1971 0.975 12 12
CN Cyano radical 1 Σ 2154 2042 0.948 13 13
N2 Nitrogen diatomic 1 Σg 2447 2330 0.952 14 14
PH phosphorus monohydride 1 Σ 2342 2276 0.972 15 15
    1 Σ 2354 2319 0.985 15 16
PN Phosphorus mononitride 1 Σ 1404 1323 0.942 16 17
P2 Phosphorus diatomic 1 Σg 808 775 0.960 17 18
OH Hydroxyl radical 1 Σ 3703 3570 0.964 18 19
LiO lithium oxide 1 Σ 821 799 0.974 19 20
BeO beryllium oxide 1 Σ 1554 1435 0.923 20 21
BO boron monoxide 1 Σ 1921 1862 0.969 21 22
CO Carbon monoxide 1 Σ 2214 2143 0.968 22 23
NaO sodium monoxide 1 Σ 481     23 24
MgO magnesium oxide 1 Σ 826 775 0.939 24 25
SiO Silicon monoxide 1 Σ 1260 1230 0.976 25 26
HS Mercapto radical 1 Σ 2666 2599 0.975 26 27
BeS beryllium sulfide 1 Σ 1012 986 0.974 27 28
CS carbon monosulfide 1 Σ 1305 1272 0.975 28 29
SO Sulfur monoxide 1 Σ 1153 1138 0.987 29 30
    1 Σ 1152 1054 0.915 29 31
MgS magnesium sulfide 1 Σ 527 523 0.993 30 32
SiS silicon monosulfide 1 Σ 744 744 1.000 31 33
S2 Sulfur diatomic 1 Σg 713 720 1.010 32 34
HF Hydrogen fluoride 1 Σ 4086 3961 0.970 33 35
LiF lithium fluoride 1 Σ 911 896 0.984 34 36
CF Fluoromethylidyne 1 Σ 1297 1286 0.992 35 37
F2 Fluorine diatomic 1 Σg 1045 894 0.855 36 38
NaF sodium fluoride 1 Σ 525 529 1.008 37 39
AlF Aluminum monofluoride 1 Σ 777 793 1.020 38 40
SiF silicon monofluoride 1 Σ 829 848 1.022 39 41
SF Monosulfur monofluoride 1 Σ 824 829 1.006 40 42
HCl Hydrogen chloride 1 Σ 2934 2886 0.984 41 43
LiCl lithium chloride 1 Σ 642 634 0.988 42 44
BCl boron monochloride 1 Σ 818 829 1.013 43 45
ClO Monochlorine monoxide 1 Σ 854 843 0.986 44 46
ClF Chlorine monofluoride 1 Σ 787 773 0.983 45 47
NaCl Sodium Chloride 1 Σ 356 361 1.014 46 48
AlCl Aluminum monochloride 1 Σ 455 478 1.050 47 49
SCl sulfur monochloride 1 Σ 560 577 1.031 48 50
Cl2 Chlorine diatomic 1 Σg 539 554 1.029 49 51
BeH2 beryllium dihydride 2 Σu 2261 2159 0.955 50 52
    3 Πu 727 698 0.960 50 53
MgH2 magnesium dihydride 2 Σu 1639 1572 0.959 51 54
    3 Πu 437 440 1.007 51 55
SiH2 silicon dihydride 1 A1 2043 1996 0.977 52 56
    2 A1 1023 999 0.977 52 57
    3 B2 2043 1993 0.976 52 58
NH2 Amino radical 1 A1 3352 3219 0.960 53 59
    2 A1 1536 1497 0.975 53 60
    3 B2 3440 3301 0.960 53 61
HCN Hydrogen cyanide 1 Σ 3439 3312 0.963 54 62
    2 Σ 2202 2089 0.949 54 63
    3 Π 762 712 0.935 54 64
HNC hydrogen isocyanide 1 Σ 3802 3653 0.961 55 65
    2 Σ 2107 2029 0.963 55 66
    3 Π 473 477 1.009 55 67
HCP HCP 1 Σ 3348 3217 0.961 56 68
    2 Σ 1343 1278 0.952 56 69
    3 Π 721 674 0.935 56 70
HPO HPO 1 A' 2085 2095 1.005 57 71
    2 A' 1223 1188 0.971 57 72
    3 A' 1004 986 0.982 57 73
H2O Water 1 A1 3805 3657 0.961 58 74
    2 A1 1635 1595 0.975 58 75
    3 B2 3906 3756 0.962 58 76
LiOH lithium hydroxide 1 Σ 3994 3688 0.923 59 77
    2 Σ 965 871 0.902 59 78
    3 Π 361 257 0.710 59 79
BeOH beryllium monohydroxide 2 A' 1292 1246 0.964 60 80
HBO Boron hydride oxide 1 Σ 2893 2850 0.985 61 81
    2 Σ 1869 1826 0.977 61 82
    3 Π 776 756 0.975 61 83
HNO Nitrosyl hydride 1 A' 2846 2684 0.943 62 84
    2 A' 1667 1565 0.939 62 85
    3 A' 1566 1501 0.958 62 86
HO2 Hydroperoxy radical 1 A' 3600 3436 0.954 63 87
    2 A' 1436 1392 0.969 63 88
    3 A' 1165 1098 0.942 63 89
NaOH sodium hydroxide 1 Σ 3950 3637 0.921 64 90
    2 Σ 565 540 0.956 64 91
    3 Π 133 300 2.255 64 92
H2S Hydrogen sulfide 1 A1 2681 2615 0.976 65 93
    2 A1 1209 1183 0.978 65 94
    3 B2 2694 2626 0.975 65 95
HBS hydrogen boron sulfide 1 Σ 2838 2736 0.964 66 96
    2 Σ 1188 1172 0.987 66 97
HCF Fluoromethylene 1 A' 2760 2643 0.958 67 98
    2 A' 1440 1403 0.975 67 99
    3 A' 1201 1189 0.990 67 100
HOF Hypofluorous acid 1 A' 3731 3578 0.959 68 101
    2 A' 1409 1362 0.967 68 102
    3 A' 983 893 0.909 68 103
HOCl hypochlorous acid 1 A' 3770 3609 0.957 69 104
    2 A' 1266 1239 0.978 69 105
    3 A' 740 724 0.978 69 106
BH3 boron trihydride 2 A2" 1161 1148 0.988 70 107
    3 E' 2690 2602 0.967 70 108
    4 E' 1206 1197 0.992 70 109
AlH3 aluminum trihydride 1 A1' 1943 1900 0.978 71 110
    2 A2" 712 698 0.980 71 111
    3 E' 1949 1883 0.966 71 112
    4 E' 800 783 0.979 71 113
C2H2 Acetylene 1 Σg 3511 3374 0.961 72 114
    2 Σg 2068 1974 0.954 72 115
    3 Σu 3413 3289 0.964 72 116
    4 Πg 656 612 0.933 72 117
    5 Πu 766 730 0.953 72 118
SiH3 Silyl radical 1 A1 2195 2136 0.973 73 119
    2 A1 766 728 0.950 73 120
    3 E 2233 2185 0.978 73 121
    4 E 938 922 0.983 73 122
NH3 Ammonia 1 A1 3467 3337 0.963 74 123
    2 A1 1051 950 0.904 74 124
    3 E 3583 3444 0.961 74 125
    4 E 1670 1627 0.974 74 126
PH3 Phosphine 1 A1 2387 2323 0.973 75 127
    2 A1 1018 992 0.974 75 128
    3 E 2393 2328 0.973 75 129
    4 E 1139 1118 0.981 75 130
H2CO Formaldehyde 1 A1 2879 2782 0.966 76 131
    2 A1 1820 1746 0.959 76 132
    3 A1 1535 1500 0.977 76 133
    4 B1 1203 1167 0.970 76 134
    5 B2 2933 2843 0.969 76 135
    6 B2 1269 1249 0.984 76 136
H2O2 Hydrogen peroxide 1 A 3766 3599 0.956 77 137
    2 A 1439 1402 0.974 77 138
    3 A 950 877 0.923 77 139
    4 A 381 371 0.974 77 140
    5 B 3764 3608 0.958 77 141
    6 B 1327 1266 0.954 77 142
H2CS Thioformaldehyde 1 A1 3061 2971 0.971 78 143
    2 A1 1494 1456 0.974 78 144
    3 A1 1087 1059 0.974 78 145
    4 B1 1030 990 0.961 78 146
    5 B2 3142 3025 0.963 78 147
    6 B2 1005 991 0.986 78 148
H2S2 Disulfane 1 A 2619 2556 0.976 79 149
    2 A 889 882 0.992 79 150
    3 A 501 515 1.027 79 151
    4 A 431 417 0.969 79 152
    5 B 2621 2559 0.976 79 153
    6 B 890 878 0.986 79 154
CH4 Methane 1 A1 3027 2917 0.964 80 155
    2 E 1559 1534 0.984 80 156
    3 T2 3129 3019 0.965 80 157
    4 T2 1341 1306 0.974 80 158
SiH4 Silane 1 A1 2241 2187 0.976 81 159
    2 E 979 975 0.996 81 160
    3 T2 2245 2191 0.976 81 161
    4 T2 923 914 0.991 81 162
CH2NH Methanimine 1 A' 3431 3263 0.951 82 163
    2 A' 3105 3024 0.974 82 164
    3 A' 3011 2914 0.968 82 165
    4 A' 1711 1638 0.957 82 166
    5 A' 1492 1452 0.973 82 167
    6 A' 1371 1344 0.981 82 168
    7 A' 1075 1058 0.985 82 169
    8 A" 1167 1127 0.966 82 170
    9 A" 1103 1061 0.961 82 171
NH2OH hydroxylamine 1 A' 3816 3650 0.956 83 172
    2 A' 3440 3294 0.958 83 173
    3 A' 1666 1605 0.963 83 174
    4 A' 1398 1353 0.968 83 175
    5 A' 1147 1115 0.972 83 176
    6 A' 929 895 0.963 83 177
    7 A" 3516 3359 0.955 83 178
    8 A" 1328 1295 0.974 83 179
    9 A" 411 386 0.939 83 180
CH3F Methyl fluoride 1 A1 3028 2930 0.968 84 181
    2 A1 1488 1464 0.984 84 182
    3 A1 1049 1049 1.000 84 183
    4 E 3106 3006 0.968 84 184
    5 E 1494 1467 0.982 84 185
    6 E 1195 1182 0.989 84 186
SiH3F monofluorosilane 1 A1 2253 2206 0.979 85 187
    2 A1 996 990 0.994 85 188
    3 A1 861 872 1.012 85 189
    4 E 2257 2196 0.973 85 190
    5 E 967 956 0.988 85 191
    6 E 727 728 1.001 85 192
CH3Cl Methyl chloride 1 A1 3070 2966 0.966 86 193
    2 A1 1378 1355 0.983 86 194
    3 A1 713 732 1.027 86 195
    4 E 3165 3042 0.961 86 196
    5 E 1483 1455 0.981 86 197
    6 E 1027 1015 0.989 86 198
SiH3Cl chlorosilane 1 A1 2256 2201 0.975 87 199
    2 A1 954 949 0.995 87 200
    3 A1 531 551 1.037 87 201
    4 E 2266 2195 0.969 87 202
    5 E 960 954 0.994 87 203
    6 E 660 664 1.006 87 204
C2H4 Ethylene 1 Ag 3138 3026 0.965 88 205
    2 Ag 1690 1623 0.960 88 206
    3 Ag 1381 1342 0.972 88 207
    4 Au 1065 1023 0.960 88 208
    5 B1u 3125 2989 0.956 88 209
    6 B1u 1479 1444 0.976 88 210
    7 B2g 987 940 0.952 88 211
    8 B2u 3222 3105 0.964 88 212
    9 B2u 836 826 0.988 88 213
    10 B3g 3194 3086 0.966 88 214
    11 B3g 1246 1217 0.977 88 215
    12 B3u 980 949 0.969 88 216
N2H4 Hydrazine 1 A 3552 3398 0.957 89 217
    2 A 3460 3329 0.962 89 218
    3 A 1687 1642 0.973 89 219
    4 A 1329 1275 0.959 89 220
    5 A 1113 1076 0.967 89 221
    6 A 808 780 0.966 89 222
    7 A 440 377 0.856 89 223
    8 B 3558 3350 0.941 89 224
    9 B 3451 3314 0.960 89 225
    10 B 1676 1628 0.972 89 226
    11 B 1299 1275 0.982 89 227
    12 B 988 966 0.978 89 228
CH3OH Methyl alcohol 1 A' 3836 3681 0.960 90 229
    2 A' 3106 3000 0.966 90 230
    3 A' 2990 2844 0.951 90 231
    4 A' 1510 1477 0.978 90 232
    5 A' 1482 1455 0.982 90 233
    6 A' 1372 1345 0.981 90 234
    7 A' 1080 1060 0.981 90 235
    8 A' 1043 1033 0.990 90 236
    9 A" 3034 2960 0.976 90 237
    10 A" 1497 1477 0.987 90 238
    11 A" 1173 1165 0.993 90 239
    12 A" 294 200 0.681 90 240
CH3SH Methanethiol 1 A' 3133 3000 0.958 91 241
    2 A' 3050 2931 0.961 91 242
    3 A' 2671 2597 0.972 91 243
    4 A' 1489 1475 0.991 91 244
    5 A' 1359 1335 0.982 91 245
    6 A' 1097 1074 0.979 91 246
    7 A' 798 803 1.006 91 247
    8 A' 698 708 1.014 91 248
    9 A" 3133 3000 0.958 91 249
    10 A" 1476 1430 0.969 91 250
    11 A" 974 976 1.002 91 251
CH3NH2 methyl amine 1 A' 3498 3361 0.961 92 252
    2 A' 3054 2961 0.970 92 253
    3 A' 2964 2820 0.951 92 254
    4 A' 1664 1623 0.976 92 255
    5 A' 1499 1473 0.982 92 256
    6 A' 1461 1430 0.979 92 257
    7 A' 1173 1130 0.964 92 258
    8 A' 1055 1044 0.989 92 259
    9 A' 831 780 0.938 92 260
    10 A" 3571 3427 0.960 92 261
    11 A" 3088 2985 0.967 92 262
    12 A" 1518 1485 0.978 92 263
    13 A" 1347 1335 0.991 92 264
    14 A" 975     92 265
    15 A" 299 268 0.895 92 266
B2H6 Diborane 1 Ag 2619 2530 0.966 93 267
    2 Ag 2178 2088 0.959 93 268
    3 Ag 1205 1183 0.982 93 269
    4 Ag 800 790 0.987 93 270
    5 Au 850 833 0.980 93 271
    6 B1g 2692 2596 0.964 93 272
    7 B1g 940 915 0.973 93 273
    8 B1u 1994 1930 0.968 93 274
    9 B1u 991 973 0.981 93 275
    10 B2g 1859 1760 0.947 93 276
    11 B2g 894 860 0.962 93 277
    12 B2u 2707 2609 0.964 93 278
    13 B2u 954 949 0.995 93 279
    14 B2u 362 369 1.018 93 280
    15 B3g 1021 1020 0.999 93 281
    16 B3u 2606 2520 0.967 93 282
    17 B3u 1716 1603 0.934 93 283
    18 B3u 1198 1172 0.978 93 284
C2H6 Ethane 1 A1g 3025 2954 0.977 94 285
    2 A1g 1423 1388 0.975 94 286
    3 A1g 995 995 1.000 94 287
    4 A1u 304 289 0.952 94 288
    5 A2u 3026 2896 0.957 94 289
    6 A2u 1413 1379 0.976 94 290
    7 Eg 3069 2969 0.967 94 291
    8 Eg 1503 1468 0.977 94 292
    9 Eg 1223 1190 0.973 94 293
    10 Eu 3094 2985 0.965 94 294
    11 Eu 1506 1469 0.975 94 295
    12 Eu 827 822 0.994 94 296
Si2H6 disilane 1 A1g 2221 2152 0.969 95 297
    2 A1g 928 909 0.980 95 298
    3 A1g 423 434 1.027 95 299
    4 A1u 138 131 0.951 95 300
    5 A2u 2212 2154 0.974 95 301
    6 A2u 855 844 0.987 95 302
    7 Eg 2218 2155 0.972 95 303
    8 Eg 946 929 0.982 95 304
    9 Eg 634 625 0.986 95 305
    10 Eu 2228 2179 0.978 95 306
    11 Eu 960 940 0.978 95 307
    12 Eu 376 379 1.010 95 308

How do we calculate the scaling factor?

Histogram of vibrational frequency ratios

Ratios greater than 1.35 are in the 1.35 bin. Ratios less than 0.7 are in the 0.7 bin.

40 160 1 1 1 1 1 1 1 1 1 1 1 1 1 1
40 140 1 1 1 1 1 1 1 1 1 1 1 1 1 1
40 120 1 1 1 1 1 1 1 1 1 1 1 1 1 1
40 100 1 1 1 1 1 1 1 1 1 1 1 1 1 1
40 80 1 1 1 1 1 1 1 1 1 1 1 1 1 1
40 60 1 1 1 1 1 1 1 1 1 1 1 1 1 1
40 40 1 1 1 1 1 1 1 1 1 1 1 1 1 1
40 20 1 1 1 1 1 1 1 1 1 1 1 1 1 1
40 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1
0.70 0.75 0.80 0.85 0.90 0.95 1.00 1.05 1.10 1.15 1.20 1.25 1.30 1.35
Ratio of experimental frequency to calculated frequency